ADA4625-2ARDZ-R7 datasheet(28/35 Pages) AD

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ADA4625-1/ADA4625-2

Data Sheet

Rev. A | Page 28 of 35

It is important to distinguish between the signal gain and the

noise gain (NG) because the noise gain characteristics

determine the net circuit stability. The noise gain has the same

transfer function as the noninverting signal gain, which follows:













)

)(

(

(2)

where:

RSH is the diode shunt resistance.

CIN is the total input capacitance consisting of the sum of the

diode shunt capacitance (CD), the input capacitance of the

amplifier (CDM + CCM), and the external stray capacitance.

CIN and RF produce a zero in the noise gain transfer function

and the zero frequency (fZ) is as follows:

)

)(

(

(3)

Because the photodiode shunt resistance RSH >> RF, the circuit

behavior is not impacted by the effect of the junction resistance,

and fZ simplifies to

)

(

2π

(4)

Figure 100 shows the TIA noise gain superimposed upon the open

loop gain of the amplifier. For the system to be stable, the noise gain

curve must intersect with the open loop response with a net slope

of less than 20 dB/decade. In Figure 100, the dotted line shows an

uncompensated noise gain (CF = 0 pF) intersecting with the open

loop gain at the frequency (fX) with a slope of 20 dB/decade,

indicating an unstable condition.

fGBP

FREQUENCY

UNCOMPENSATED

(CF = 0pF)

CIN

OPEN LOOP GAIN

NOISE GAIN

SIGNAL BANDWIDTH

COMPENSATED

1 +

Figure 100. Generalized TIA Noise Gain and Transfer Function

The instability caused by CIN can be compensated by adding CF to

introduce a pole at a frequency equal to or lower than fX. The pole

frequency is as follows:

2π

(5)

Setting the pole at the fX frequency maximizes the signal bandwidth

with a 45° phase margin but is marginal for stability, as indicated by

the dashed line. Because fX is the geometric mean of fZ and the

gain bandwidth product frequency (fGBP) of the amplifier,

calculate fX by

GBP

(6)

Substituting Equation 4 and Equation 5 into Equation 6, the CF

value that produces fX is

GBP

(7)

If 8π × RF × CIN × fGBP >> 1, Equation 7 simplifies to

GBP

(8)

Adding CF also sets the signal bandwidth at fP. Substitute

Equation 8 into Equation 5 and rearrange the equation for the

signal bandwidth in terms of fGBP, RF, and CIN:

GBP

(9)

Notice the attainable signal bandwidth is a function of the time

constant RFCIN and the fGBP of the amplifier. To maximize the

signal bandwidth, choose an op amp with high bandwidth and

low input capacitance, and operate the photodiode in reverse

bias to reduce its junction capacitance.

Because the input current noise of the FET input op amp is

negligible, and the shot noise of the photodiode is negligible

due to the filtering effect of the shunt capacitance, the dominant

sources of output noise in the wideband photodiode TIA circuit

are the input voltage noise of the amplifier eN and the thermal

noise generated by RF.

At low frequencies, the circuit noise gain is 1 + RF/RSH. At

frequencies equal to or greater than fZ, the noise gain begins to

increase and plateau when the gain is 1 + CIN/CF (see Figure 100).

In addition, the noise bandwidth frequency, fN (where the

compensated noise gain intersecting the open loop gain), can

be estimated by

GBP

)

(

(10)

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